1GB RAM might be too much. Remember, OS X is hosting Parallels which is running Windows. Any RAM you assign to the guest OS will not be available for the host OS, and everything starts to slow down.
It's a mistake many newcomers to virtualization make, thinking that the more RAM they add to the guest, the faster it will be. Just last week, I watched a colleague at work struggling with a slowly responding Linux VM. I checked his settings and he'd pushed the guest RAM up to 1.5GB. I got him to reduce it to 512MB and it was much better. There seems to be a sweet spot at about 1/4-1/3 the host's RAM.
Anyway, I haven't tried Netflix Watch Now in Parallels, but I have in VMWare's Fusion, with 512MB. It was fine.